@kathy79,
That's a very odd sentence, and i do wonder if it was written by a native speaker.
However, in this sense, wake means "the track left by a moving body (as a ship) in a fluid (as water); broadly : a track or path left" (that's from the Merriam-Webster online dictionary). So the colorful wake of London life is a figurative usage meaning in the path of London life, the colorful path of London life.